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Probability
The probability of a certain event is a number expressing the likelihood that a specific event will occur, expressed as the ratio of the number of actual occurrences to the number of possible occurrences. In mathematics, it is a measure of how often an event will happen and is the basis of statistics.
14,643 Questions
Odds of rolling doubles with three dice?
There are 36 possible combinations of unique dice rolls (where order doesn't matter, so sorted/deduped). 6 of these are potentially doubles. The total odds are 1/6 (~16.7%). This is because the probability that any of the two die matched any of the other two dice is really just the probability that a die is the same as another die, which is 1/6. Think about it this way, if you rolled two dice the probability that the first one is the same as the second one is 1/6. If you rolled a one, and then rolled a second die and it didn't come up as the first one, but then you rolled a third one you'll find that the probability that doubles occurred is the probability that the first one matches the third one, OR the second one matches the third one IIF the second one did not match the first one, but because they're independent events it's still just what's the probability that doubles occurred between the comparison rather than the set.
This does not take into account triplets being considered doubles. If the potential for triplets is considered (the probability that any two die will have the same value), this becomes a very simple problem because it deals with the likelihood that something can't occur in any form rather than the likelihood that a specific subset will occur. It's simply the probability (after sorting) that the first one is like the second one, or the second one is like the third one. When you think about that, that's really just the probability that all numbers will be different. This means we only have to care about two. The probability that the second is different is 5/6, while the probability that the third is different than both of the first two is 4/6. That makes the probability that no two are alike 5/6 by 4/6. This means that the probability that AT LEAST two are alike is 1 - (5/6 * 4/6), which is 44.444..%. It's an extremely simplified version of the birthday problem.
How many ways can you arrange 8 different crates on a shelf if they are placed from left to right?
8!=8*7*6*5*4*3*2*1=40320 ways
Is the F distribution used to test whether two samples are from population with equal variances?
It can be used for that purpose.
If you draw enough balls, without replacement, the probability is 1.
The answer depends on
- how many balls are drawn, and
- whether or not they are replaced.
Unfortunately, your question gives no information on these matters.
What is the change of two people having a baby girl?
Not so sure about the "change" of two "peole" but the chance of two people having a baby girl is 0.48 (approx).
This assumes that these are people of child-bearing age, with average genetic characteristics.
What is the prabability of getting an odd number when rolling a single 6 sided die?
Look at a 6 sided die. As the name implies, there are 6 sides. The sides are numbered 1,2,3,4,5, and 6. How many of those numbers are odd? Take that number and divide it by the total number of sides on the die. That will give you the probability of getting an odd number when rolling a single 6 sided die.
If Tim lost one-eighth of his marbles and he had 56 how many did he lose?
1/8 of 56 is 7 since 7x8=56
So Tim lost 7 marbles.
What is the likelihood that an event will occur?
Trick Question; events can have anywhere between 0% and 100% chance of happening, so therefor saying "an event" as an example would in fact be unanswerable.
Fact Man to the rescue.
What does the area under the curve equal?
The are under the curve on the domain (a,b) is equal to the integral of the function at b minus the integral of the function at a
What does a union b always equal to?
the combination of all elements of either set into the new combined set.
What is the probability of drawing a diamond or a red card from a 52 card deck?
"Neither card is red" is the same as "both cards are black". The probability that the first card is black is 26 out of 52, or 1/2. Given that the first card is black, there are 51 cards remaining, of which 25 are black; thus the conditional probability that the second card is also black is 25/51. The probability that both cards are black is the product of these two probabilities: 1/2 * 25/51 = 25/102, or about 24.51%.
How many ways can the letters in square be arranged?
The letters of the word SQUARE can be arranged in 6! = 720 orders.
What is something that is a certain outcome?
That the outcome will be one of all possible outcomes.
For example, that an integer will be odd or even.
A fair coin is flipped four times Give the probability distribution for the number of heads?
P(0 heads) = 1/16
P(1 head ) = 1/4
P(2 heads) = 6/16 = 3/8
P(3 heads) = 1/4
P(4 heads) = 1/16
Is it desirable to have a two sample test with equal sizes?
If they are not matched pairs, it does not really matter. If the combined sample size is fixed (because of costs, say) then it is better to have a larger sample where more variability is expected.
What are the odds of rolling a four 3 times in a row using two dice?
Assuming fair dice:
With 3 dice there are 6 x 6 = 36 possible permutations (the two dice can be identified and are independent of each other).
Of these there are 3 ways (1+3, 2+2, 3+1) of getting four.
Probability of getting a four with 2 dice on one roll = 4/36 = 1/9
As rolls are independent, the probability of getting 4 with 2 dice 3 times in a row is 1/9 x 1/9 x 1/9 = 1/729
So the odds of it are 728 to 1 against, ie 1 in 729 or about 0.14 %.
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How do you calculate the probability for a group of several independent events?
You multiply together their individual probabilities.
